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The number of borrowers defaulting on federal student loans has risen substantially, highlighting concerns that rising college costs, low graduation rates and poor job prospects are getting more and more students over their heads in debt.

The national two-year cohort default rate rose to 8.8 percent last year, from 7 percent in fiscal 2008, according to figures released Monday by the Department of Education.

The latest figures show the percentage of the more than 3.6 million borrowers whose first payments came due in the year starting October 2008 — at the height of the financial crisis — and who defaulted before Sept. 30, 2010.

More borrowers in that group have likely defaulted since last fall. Next year the department will begin using three-year default rates — considered a more accurate measure — to determine which institutions lose eligibility to enroll students who have borrowed from the government.

The latest figures show substantial variations by state, ranging from default rates of 3.4 percent at institutions in Montana and North Dakota to 16 percent among borrowers at colleges in Arizona.

“These hard economic times have made it even more difficult for student borrowers to repay their loans, and that’s why implementing education reforms and protecting the maximum Pell grant is more important than ever,” U.S. Secretary of Education Arne Duncan said in a press release.

The federal default rate remains substantially below its peak of more than 20 percent in the early 1990s, before a series of reforms in government lending. But after years of steady declines it has now risen four straight years and is almost double its trough of 4.6 percent in 2005.

The figures come as a stalled economy is hitting student borrowers from two sides — forcing cash-strapped state institutions to raise tuition, and making it harder for graduates to find jobs. But there are also new income-based repayment options implemented by the Obama administration, and new, tighter regulations for-profit schools that will likely lower default rates at for-profit colleges by pressing them to close failing programs and enroll fewer students who are unlikely to succeed.

But for now, the default rate at for-profit schools is surging. Breaking down the numbers by type of institution, the department said the default rate rose from 6 percent to 7.2 percent at public institutions, from 4 percent to 4.6 percent at private institutions, and from 11.6 percent to 15 percent at for-profit schools.

The figures released Monday cover only loans made by students from the federal government, which account for roughly 90 percent of student lending and generally have lower interest rates and higher consumer protections than private student loans.